My mac computer is connected to my corporate network via a LAN connection. When the Mac is disconnected I can connect to our corporate wireless. The wireless is more open than the LAN connection. Meaning I can go to more places on the internet that aren't blocked by our corporate firewall.

Instead of unplugging my Mac every time I want to check Facebook or Gmail, I would like to be able to set my browsers to use one specific connection while both are active.

Firefox use LAN and Safari use Wireless.

Is that even possible? Or just because the LAN is active, it defaults as the primary internet access?

I am an admin and can change any thing on the mac so that isn't an issue.

Instead of using 2 different connections which is extremely hard to configure, why not just use a VPN or a Proxy? Essentially what a VPN or proxy will do is use your existing connection to connect to a private network completely separate from the one you are using. one will generally not notice many differences between the non-VPN connection and the private VPN connection other than that some, if not all, sites that were blocked before will be unblocked.

Some proxies (like Hotspot Shield) are free and ad-supported (sometimes you will see advertisements at the top of your web page), and others like Hidemyass, which is a VPN, are paid but extremely reliable and ad-free. This may not always work though, depending on weather or not your network allows it.

another way to get around site blockages is simply to either type "HTTPS://" in front of the site URL in the address bar of your browser, or if the HTTP:// is already there, just add an S in front of the HTTP, hit enter, and you should be good to go.